Using online updating algorithms to predict speedway results.

Dawid Kałędkowski@ClickMeeting
2018-07-04

Speedway is a motorcycle sport

  • Motorbike sport on oval dirt-track
  • 4 Riders race 4 laps
  • Start signaled by tape rise and light
  • Exclusions for falling, engine failures, touching tape etc.
  • Sliding scale for scoring (3-2-1-0)

speedway track

More than 1000 events annualy (2017)

leagues

  • 1000 riders from 31 countries
  • 100 different competitions.
  • Individual competitions - Grand-Prix
  • League matches - PGE Ekstraliga, Premiership, Elitserien, Bundesliga etc.
  • Team competitions - SWC/SON
  • Pair competitions - SBP

Statistics matters

Approach to data is old-fashioned

source: sportowefakty.pl/zuzel, speedwayupdates.proboards.com, speedwayresults.com

Data gathering partially automated

  • Multiple scrapes for different pages (rvest,RSelenium and a lot of REGEXP)
  • PDF Parsers (tabulizer)
  • Approximate names matching (stringdist::amatch)
  • Web application to browse and update results (shiny, rhandsontable with RMySQL)
  • Additional verification (comparing individual sums, squads sums, team sums)

r_packages_used

Actual speedway database

  • 3 years of collecting data.
  • 10528 events in 148 competitions.
  • Almost 700k individual performances.
  • Unified rider names, competitions, places.
  • 241 Speedway stadiums with coordinates.

Analytical challange

  • Output is a ranking
  • Need for continuous updates
  • Some commonly known effects need to be examined:
    • Riders form changes in time
    • Many interactions (gate*heat*stadium)
    • Field advantage
    • Winter break

hmmm

Online Algorithms

  • Logit as underlying function

  • Model is estimated using Bayesian Approximation Method \[ \large R_i^{'} \leftarrow R_i + K * ( Y_i - \hat{Y_i} ) \]

  • Update doesn't require previous data

  • Computationaly efficient

Elo

  • Points gain depends only on ratings difference
  • First widely known algorithm
  • Very succesful in leagues for 2-player games:
    • FIFA ranking
    • US Chess Federation (USCF)
    • World Chess Federation (FIDE)

elo

source: https://www.fide.com/fide/handbook.html?id=172&view=article

Glicko (sport::glicko)

\[ \large \hat{Y_{ij}} = P(X_i>X_j) = \frac{1}{ 1 + 10^{-g(RD_{ij}) * (R_i-R_j)/400}} \]

\[ \large {R'}_i = R_i + \frac{1}{\frac{1}{{RD}^2_{i}} + \frac{1}{d^2_i}} * \sum_j{g(RD_j) * (Y_{ij} - \hat{Y_{ij}}) } \] \[ \large {RD'}_i = \sqrt{(\frac{1}{{RD}^2_{i}} + \frac{1}{d^2_i}})^{-1} \]

  • New parameter RD - rating deviation

Glicko2 (sport::glicko2)

\[ \large \hat{Y_{ij}} = \frac{1}{1 + e^{-g(\phi_{ij})*(\mu_i - \mu_j)} } \]

\[ \large {\phi'}_i = \frac{1}{\sqrt{ \frac{1}{ { {\phi_i}^2 + {\sigma'_i}^2}} + \frac{1}{v} }} \]

\[ \large {\mu'_i} = \mu_i + {\phi'}_i * \sum_j{g(\phi_j)*(Y_{ij} - \hat{Y_{ij}})} \]

  • New parameter \( \sigma \) measures volatility

Bayesian Bradley Terry (sport::bbt)

\[ \large \hat{Y_{ij}} = P(X_i>X_j) = \frac{e^{R_i/c_{i_j}}}{e^{R_i/c_{ij}} + e^{R_j/c_{ij}}} \]

\[ \large {R'}_i = R_i + \sum_j{\frac{RD_i^2}{c_{ij}}*(Y_{ij} - \hat{Y_{ij}})} \] \[ \large {RD'}_i = RD_i * [ 1 - \frac{RD_{ij}^2}{RD_i^2}\sum_j{ \gamma_j * (\frac{RD_i}{c_{ij}})^2* \hat{Y_{ij}}\hat{Y_{ji}} } ] \]

  • Able to measure individual ratings within teams.

Dynamic Bayesian Logit (sport::bdl)

  • Algorithm has learning rate parameter - low at stationary regions and high in regions of nonstationarity to allow tracking.
  • Able to estimate many induvidual specific parameters

\[ \large \beta_t = {\beta_{t-1}} + \eta_t \]

\[ \large Y_t = \frac{e^{z}}{1+e^{z_{t}}} \]

\[ \small z_t = \beta_{it}^Tx_{it}-\beta_{jt}^Tx_{jt} \]

\[ \small w_t = w_{t-1} + {\sum{_t}} x_t \]

`sport` - package for sport analytics

  • Installation - package available on github.com/gogonzo/sport. Still under development, far from final product but syntax won't change. 

# devtools::install_github("gogonzo/sport")
library(sport)

  • To estimate riders (rider_name) abilities with given outputs (rank) nested within particular heats (id)

list_glicko   <- glicko_run( formula = rank|id ~ rider_name , 
                             data    = gpheats )

`sport` - package for sport analytics

Output contains:

  • r data.frame with all historical parameters (ratings and ratings deviations) estimation
  • pairs data.frame with pair combination within heats with estimated winning probability
  • final_r actual ratings estimations
  • final_rd actual ratings deviations

names( list_glicko )

[1] "r"        "pairs"    "final_r"  "final_rd"


head( list_glicko$r )
tail( list_glicko$pairs )

Methods perform similarly.

Ensemble models doesn't improve performance.

speedway track

  • xgBoost, Random Forests nor Boosted trees didn't improve accuracy.
  • Additional variables have no additional predictive abilities.

Non-rating vars contribution <5%

The Best speedway riders

ratings

TODO

  • Searching for perfect predictive model.
  • Improve sport package.
  • Simulate events results.
  • Promote data-science in speedway.

References

References:

Thank you




github.com/gogonzo

dawid.kaledkowski@clickmeeting.com

linkedin.com/in/dawidkaledkowski/